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Select all of the points that are solutions to the system of linear inequalities that is listed below 10x + 4y < 12 8x -3y > 20

User Wobbles
by
7.8k points

1 Answer

7 votes

Answer:

(3, -8) and (2, -10)

Explanation:

Given


10x + 4y < 12


8x - 3y > 20

Required

Select the true coordinate points in (3, -8) (2, 5) (-5, 1) (10, 3) (2, -10)

(3, -8)

x = 3 and y = -8


10x + 4y < 12


10 * 3 + 4 * -8 < 12


30 - 32 < 12


-2 < 12 --- True


8x - 3y > 20


8 * 3 - 3 * -8> 20


24 +24> 20


48> 20 --- True

(2, 5)

x = 2 and y = 5


10x + 4y < 12


10 * 2 + 4 * 5 < 12


20 + 20 < 12


40 < 12 --- False (No need to check the other inequality)

(-5, 1)

x = -5 and y = 1


10x + 4y < 12


10 * -5 + 4 * 1 < 12


-46 < 12 --- True


8x - 3y > 20


8 * -5 - 3 * 1 > 20


-43 > 20 --- False

(10, 3)

x = 10 and y = 3


10x + 4y < 12


10 * 10 + 4 * 3 < 12


112 < 12 --- False (No need to check the other inequality)

(2, -10)

x = 2 and y = -10


10x + 4y < 12


10 * 2 + 4 * -10 < 12


-20 < 12 --- True


8x - 3y > 20


8 * 2 - 3 * -10 > 20


46 > 20 --- True

Hence, the solution to the inequalities are:

(3, -8) and (2, -10)

User Yusuf
by
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